Given that I did not explicitly code for any other contraints, I'm struggling to understand why the model fit of the third model is not approximating that of the first model (single sample) if there are no between-group constraints in the third model. Does Mplus automatically place constraints on any parameters (e.g., variances, errors)?

In 3, it looks like some parameters are still constrained. If they were all unconstrained, the degrees of freedom would be 6262. They are not. See TECH1 to find the parameters that are still constrained to be equal.